Finite Group DatabasebetaFinite Group Databasebeta| order | 8649 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C312 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #15668332 |
| commutator, hypocenter | C312 | C9 |
| Fitting, socle | C3×C312 | C3 |
| LCS | G ▷ C312 | |
| UCS | C1 ◁ C3 | |
102 conjugacy classes of subgroups.
Polycyclic presentation:
3,31^2,3|a^3=d,b^a=b^25,c^a=c^25969 conjugacy classes — view the full character table.
| maximal subgroup of | #31772344, #31772346, C2×#22575710, … |
| maximal normal subgroup of | #31772344, #31772346, C2×#22575710 |
| maximal quotient of | C2×#22575710, C22⋊#22575710 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8649, 7);